Motor condition and performance analyzer

ABSTRACT

A motor performance analyzer senses currents and voltages applied to the motor, converts the sensed signals to digital data signals, and stores the digital data signals. The analyzer includes a processor for evaluating the digital data and a display for alerting a user or technician to potential motor problems, or to developing problems, including winding faults and broken rotor bars. Advanced signal processing techniques are used to further evaluate stored data and to provide trending information.

FIELD OF THE INVENTION

The present invention generally pertains to a device and method forevaluating and reporting motor condition and performance and moreparticularly, to an improved method and apparatus for evaluating motorperformance and assessing motor condition while the motor is operating.

BACKGROUND OF THE INVENTION

Motors, particularly electrical motors, play a key role in industry.Such motors are used to drive fans, pumps, compressors, valves, and manyother machines. It is potentially very costly to allow a significantproblem to go on unnoticed in either the motor or the motor drivenmachine. It is also costly and very time consuming to attempt to repaira nonexistent problem. With present methods of analyzing motorperformance, these costly situations often occur. Thus there is a needfor an improved diagnostic method and apparatus for use with motors andmotor driven machines.

Prior art motor monitors do not report exact shaft speed, comprehensivemotor condition, or efficiency of a continuously running motor withoutthe use of intrusive sensors. Such prior art monitors also do notprovide automatic probe misplacement detection and correction, nor dothey statistically analyze data on a per load basis, to provide ameaningful view.

Prior art motor monitors also have serious deficiencies in measuring theexact speed of an electric motor. Generally, the motor shaft speed ismeasured in one of several ways, all of which are very inconvenient to auser. One method of measuring shaft speed is to use a tachometerattached to a shaft of the motor. This requires a mechanical connectionwhich, in turn, mandates shutting the motor down. Alternatively, areflective tape or a notch can be placed on the shaft to provide aonce-per-revolution phase reference and speed indicator. However, inaddition to requiring a motor shut down, the speed accuracy is limitedbecause the timing sample occurs only once per shaft revolution. Anothermethod of determining shaft speed is to calibrate the motor driver tomeasure shaft speed based on load and torque. This is an indirectmeasurement, requires software specialized to the particular motor anddrive, and is only suitable for use on a very small number of motors.

Prior art motor monitors for detecting winding faults require the use ofcoils intrusively placed within the motor, or alternately, monitoringthe neutral return line for radio frequency evidence of arcing. Thesemonitors require extra hardware beyond the normally used three currentand three voltage probes. Additionally, in most motors the neutral wireis unavailable. Accordingly, to implement comprehensive detection, allthree electrical leads have to be monitored with high frequency probesin addition to the usual power frequency probes. This involves multipleadditional sensors and channels, high frequency sensors, and extrasignal conditioning.

Prior art motor monitors for detecting broken rotor bars generallysearch for sidebands of the first harmonic of the synchronous frequencyfor detecting broken rotor bars. This method of detection is not totallyreliable because torque variations in the load as well as the use ofcertain external equipment give rise to interfering sidebands. Forexample, the use of belt drives can produce such interfering tones.Also, air gap asymmetries between the rotor and stator can give rise toartifactual tones in that region of the spectrum.

Another shortcoming of prior art motor monitors is the need to take themotor off-line in order to ascertain resistive and inductive unbalance.This is a great inconvenience when dealing with continuous-duty motors.In addition, the off-line measurements may not be truly representativeof the on-line resistive or inductive balance, since operationalstresses may significantly change the state of balance. Further, priorart motor monitors for measuring efficiency require a dynamometer tomeasure the load.

The present invention provides a motor monitor which measures a motor'sefficiency without the requirement of a dynamometer. In addition, thepresent invention performs two unique functions which improve theefficiency measurement: (a) correcting for unbalance in the power sourcevoltage; and (b) compensating for line loss. The present inventionprovides a probe configuration for obtaining motor data and a processorfor analyzing the motor data. A memory is included for storing motordata (e.g., in a database), which allows for comparisons to be madebetween the motor's present condition and performance and motorhistorical data to determine the presence of trends, and data on similar"sister" motors to ascertain normality with respect to a population ofsimilar motors. The database accumulates knowledge about the motor,which may be sorted by load. The information provided by the presentinvention is useful for changing operating load, scheduling maintenance,planning for replacement, or even shutting down, as is appropriate.Furthermore, the system compares multiple motors under similar operatingconditions so that comparisons can be made, which are useful, forinstance, in making purchasing decisions.

The present invention determines shaft speed, condition, and performanceof a three phase induction motor, and more specifically measures theexact shaft speed, detects stator winding shorts, detects broken rotorbars, and measures output and efficiency using only current and voltagemeasurements, in conjunction with a knowledge of approximate shaftspeed, motor resistance, and historical electrical data from the samemotor under an uncoupled condition. In addition, the present inventionprovides features of great convenience to a user which prior art systemsdo not offer, such as automatic probe check and software correction formisplaced probes.

The present invention can be used to provide either on-line continuousmonitoring of condition and performance, or as a periodic inspectiontool. The present invention also provides detailed analysis capabilityfor intensive diagnostic work and a database for determining trends andrelative performance (compared to similar motors). The present inventionavoids the limitations and problems with the prior art by providing new,meaningful representations of the data, comparing results withhistorical data and sister motors and by providing on-line monitoring orperiodic inspection functions, as well as automatic probe misplacementdetection and correction. Algorithms are implemented to preciselydetermine motor speed, winding faults, and broken rotor bars fromnonintrusive current measurement, and to determine efficiency without adynamometer, by using a reasonable generic estimate of minor motorlosses, in conjunction with prior uncoupled motor data.

SUMMARY OF TEE INVENTION

Briefly stated, the present invention comprises a first method ofevaluating performance of a polyphase induction motor, the motorincluding a number of pole pairs, by using an electrical signature ofthe motor, comprising the steps of:

sensing an instantaneous current signal supplied to the motor as afunction of time for a period of time for at least one electrical phaseof the motor;

generating a Fourier transform on the sensed current signal over atleast a portion of the period of time to provide a current signalspectra;

locating a maximum frequency peak in a predetermined shaft sidebandfrequency range of the current signal spectra;

locating a frequency peak indicative of line frequency from the currentsignal spectra; and

determining a shaft speed of the motor from a difference between thelocated shaft sideband frequency maximum peak and the located linefrequency peak, taking into account the number of pole pairs of themotor.

The present invention includes a second method of evaluating performanceof a polyphase induction motor, the motor including a number of polepairs, by using an electrical signature of the motor, comprising thesteps of:

sensing an instantaneous current signal supplied to the motor as afunction of time for a period of time for at least one electrical phaseof the motor;

generating a Fourier transform on the sensed current signal over atleast a portion of the period of time to provide a current signalspectra;

locating a maximum peak in a predetermined pole-pass sideband frequencyrange of the current signal spectra;

locating a peak indicative of line frequency from the current signalspectra; and

determining a shaft speed of the motor from a difference between thelocated pole-pass sideband frequency maximum peak and the located linefrequency peak, taking into account the number of pole pairs of themotor.

The present invention also includes a third method of evaluatingperformance of a polyphase induction motor, the motor including a numberof pole pairs, using an electrical signature of the motor, comprisingthe steps of:

sensing an instantaneous current signal supplied to the motor as afunction of time for a period of time for at least one electrical phaseof the motor;

amplitude demodulating the sensed current signal to provide an amplitudedemodulated current signal as a function of time for the at least oneelectrical phase of the motor;

generating a Fourier transform on the amplitude demodulated currentsignal to provide a current signal spectra;

locating a maximum peak in a predetermined shaft frequency range of thecurrent signal spectra; and

determining a shaft speed of the motor from the located shaft frequencymaximum peak, taking into account the number of pole pairs of the motor.

The present invention includes yet a fourth method of evaluatingperformance of a polyphase induction motor, the motor including a numberof pole pairs, by using an electrical signature of the motor, comprisingthe steps of:

sensing an instantaneous current signal supplied to the motor as afunction of time for a period of time for at least one electrical phaseof the motor;

amplitude demodulating the sensed current signal to provide an amplitudedemodulated current signal as a function of time for the at least oneelectrical phase of the motor;

generating a Fourier transform on the amplitude demodulated currentsignal to provide a current signal spectra;

locating a maximum peak in a predetermined pole-pass frequency range ofthe current signal spectra; and

determining a shaft speed of the motor from the located pole-passfrequency maximum peak, taking into account the number of pole pairs ofthe motor.

The present invention includes a fifth method of evaluating performanceof a polyphase induction motor, the motor including a number of polepairs, by using an electrical signature of the motor, comprising thesteps of:

simultaneously sensing an instantaneous current signal supplied to themotor as a function of time for three electrical phases of the motor;

simultaneously sensing an instantaneous voltage supplied to the motor asa function of time for three electrical phases of the motor;

calculating a negative sequence reactance and a negative sequenceresistance from the measured voltages and currents;

determining a ratio between the negative sequence reactance and thenegative sequence resistance; and

comparing the ratio to a predetermined value whereby a predetermineddifference between the ratio and the predetermined value is indicativeof a stator winding fault.

The present invention also includes a sixth method of evaluatingperformance of a polyphase induction motor, the motor including a numberof pole pairs, by using an electrical signature of the motor, comprisingthe steps of:

simultaneously sensing an instantaneous current signal supplied to themotor as a function of time over a period of time for three electricalphases of the motor;

simultaneously sensing an instantaneous voltage supplied to the motor asa function of time over the period of time for three electrical phasesof the motor;

calculating a negative sequence reactance and a negative sequenceresistance from the measured voltages and currents; and

analyzing changes in the negative sequence resistance or the negativesequence reactance in order to detect a stator winding fault; and

measuring a load parameter of the motor over the period of time andwherein comparisons between negative sequence reactances and comparisonsbetween negative sequence resistances are made with like load parameterlevels.

The present invention further includes a method of detecting motorwinding faults of a polyphase induction motor, the motor including anumber of pole pairs, by using an electrical signature of the motor,comprising the steps of:

simultaneously sensing an instantaneous current signal supplied to themotor as a function of time over a period of time for three electricalphases of the motor;

simultaneously sensing an instantaneous voltage supplied to the motor asa function of time over the period of time for three electrical phasesof the motor;

calculating current unbalance using the sensed current signals;

calculating voltage unbalance using the sensed voltage signals;

determining a winding unbalance as a difference between the currentunbalance and the voltage unbalance, thereby removing an effect of anysource unbalance; and

comparing the winding unbalance with a predetermined value to therebydetect a motor winding fault.

The present invention also includes a method of identifying a statorfault in a polyphase induction motor, the motor including a number ofpole pairs, by using an electrical signature of the motor, comprisingthe steps of:

simultaneously sensing an instantaneous current signal supplied to themotor as a function of time over a period of time for three electricalphases of the motor;

simultaneously sensing an instantaneous voltage supplied to the motor asa function of time over the period of time for three electrical phasesof the motor;

calculating real power for each of the at least three electrical phasesof the motor using the sensed current and voltage signals;

comparing the real power for each of the three electrical phases andselecting two phases having the highest real power consumption; and

determining a motor phase having a stator fault, wherein for a motorsequence of ACB, if the two selected phases are A and B, then the phasewith the stator fault is phase B, if the two selected phases are B andC, then the phase with the stator fault is phase C, and if the twoselected phases are A and C, then the phase with the stator fault isphase A, and for a motor sequence of ACB, if the two selected phases areA and B, then the phase with the stator fault is phase A, if the twoselected phases are B and C, then the phase with the stator fault isphase B, and if the two selected phases are A and C, then the phase withthe stator fault is phase C.

The present invention also include a method of identifying broken rotorbars in a polyphase induction motor, the motor including a number ofpole pairs, by using an electrical signature of the motor, comprisingthe steps of:

simultaneously sensing an instantaneous current signal supplied to themotor as a function of time over a period of time for at least oneelectrical phase of the motor;

performing a Fourier Transform on the sensed current signal over atleast a portion of the period of time to provide a current signalspectra;

locating a peak in the current signal spectrum at a fifth harmonic ofline frequency;

locating a peak in the current signal spectrum at a fifth harmonicsideband of f_(line) (5-2·s);

locating a peak in the current signal spectrum at a fifth harmonicsideband of f_(line) (5-4·s);

locating a peak of the current signal spectrum at a fifth harmonicsideband of f_(line) (5-6·s);

identifying the sideband peaks having an amplitude within apredetermined value of an amplitude of the located fifth harmonic peak,said identified sideband peaks indicating a broken rotor bar.

The present invention also includes a method of evaluating performanceof a polyphase induction motor, the motor including a number of polepairs, by using data from an uncoupled motor condition test and dataacquired during a coupled motor condition test, comprising the steps of:

acquiring current data by simultaneously sensing an instantaneouscurrent signal supplied to the motor as a function of time for all threeelectrical phases of the motor;

acquiring voltage data by simultaneously sensing an instantaneousvoltage signal supplied to the motor as a function of time for all threeelectrical phases of the motor;

measuring individual motor stator resistances in both the uncoupledcondition and the coupled condition;

calculating slip from the coupled test data;

calculating total real power dissipated by the motor in both theuncoupled condition and the coupled condition;

calculating stator I² R loss for both the coupled condition and theuncoupled condition, as the individual currents squared multiplied bythe respective individual stator resistances corresponding to theparticular motor operating condition;

estimating loss for the uncoupled condition as the total real power lessthe stator I² R losses;

estimating core loss as a percentage of the uncoupled loss;

calculating rotor I² R loss as the total real power less the stator I² Rloss less the estimated core loss, multiplied by slip;

determining stray losses in accordance with a predetermined value basedon a machine rating of the motor; and

calculating output power as the total real power less the uncoupled lossless the stator I² R loss in the coupled condition less the rotor I² Rloss in the coupled condition and less the estimated stray losses.

The present invention also includes an apparatus for determiningelectrical performance of a polyphase motor system using an electricalsignature of the motor comprising:

current sensing means for transducing current applied to the motor andgenerating an analog current signal for at least one electrical phase ofthe motor;

analog-to-digital converter means for converting the analog currentsignals to respective digital current signals;

storage means for storing a time history of the digital current signals;

processor means for generating a Fourier transform on the stored digitalcurrent signals to provide current signal spectra;

peak locating means for locating a maximum peak in a predeterminedfrequency range of the current signal spectra and a peak indicative ofline frequency; and

arithmetic means for calculating a shaft speed of the motor from thelocated maximum peak and the line frequency peak.

The present invention further includes a means for displaying motorphasor information, which can be used in lieu of or in addition to atraditional phasor diagram. The display is a bar chart for displayingmotor voltage and current information comprising:

a horizontal axis;

a first bar chart for plotting phase to neutral voltages as bars whichgraphically represent phase-to-neutral voltages of the motor, the firstbar chart located on a first side of the horizontal axis; and

a second bar chart for plotting phase currents as bars which graphicallyrepresent phase currents of the motor, the second bar chart located on asecond, opposite side of the horizontal axis, wherein the voltage barsare positioned along the horizontal axis according to their respectivephase angles and the current bars are positioned along the horizontalaxis according to their respective phase angles, such that a powerfactor angle can be determined directly from the common axis.

The present invention also includes a method of checking placement ofvoltage and current probes on corresponding phases of a polyphaseinduction motor, comprising the steps of:

(a) simultaneously sensing an instantaneous current signal supplied tothe motor as a function of time for all three phases of the motor;

(b) simultaneously sensing an instantaneous voltage signal supplied tothe motor as a function of time for all three phases of the motor.

(c) demodulating the sensed current and voltage signals to provide anRMS value and per phase values for the three current and the threevoltage signals;

(d) comparing each of the voltage and current probe signals to a firstpredetermined value of voltage and current respectively;

(e) comparing a difference between the demodulated phase values of thethree voltage signals and a particular voltage threshold (typically 30degrees) in order to verify that any two or all of the voltage probesare not placed on the same phase;

(f) requiring that the differences between the demodulated phase valuesof the three current signals are all greater than a particular currentthreshold in order to verify that any two or all of the current probesare not placed on the same phase; and

(g) requiring that a cosine of the resulting power factor angles,respectively, of the three phases are positive and that a differencebetween a maximum and a minimum of the power factor angles of the threephases is less than a particular power factor threshold (typically 30degrees) in order to verify that none of the current probes or voltageprobes are switched or reversed.

The present invention also includes a method of checking for correctplacement of current and voltage probes on corresponding phases of apolyphase induction motor comprising the steps of:

simultaneously sensing an instantaneous current signal supplied to themotor as a function of time for all three phases of the motor;

simultaneously sensing an instantaneous voltage signal supplied to themotor as a function of time for all three phases of the motor;

demodulating the sensed current and voltage signals to provide an RMSvalue and phase values for the current and voltage signals;

calculating resulting power factor angles for all phases for each of sixpossible cases of switching of probes, viz, (i) no switching, (ii)probes A and B switched, (iii) probes B and C switched, (iv) probes Cand A switched, (v) probe A on phase C, probe B on phase A, probe C onphase B, and (vi) probe A on phase B, probe B on phase C, probe C onphase A;

calculating resulting power factor angles for all of the phases with thecurrent probes reversed;

of the six cases mentioned, selecting two cases which give power factorangles between 0 and 90 degrees for all three phases, using the powerfactor angles;

calculating total real power of the motor for each of the two selectedcases; and

recommending the two selected cases along with the values of the totalreal power, power factor angle and RMS current for each of the two casesfor switching correction.

Finally, the present invention includes a method of checking for correctplacement of current and voltage probes on corresponding phases of apolyphase induction motor comprising the steps of:

simultaneously sensing an instantaneous current signal supplied to themotor as a function of time for all three phases of the motor;

simultaneously sensing an instantaneous voltage signal supplied to themotor as a function of time for all three phases of the motor;

demodulating the sensed current and voltage signals to provide an RMSvalue and phase values for the current and voltage signals;

calculating resulting power factor angles for all phases for each of sixpossible cases of switching of probes, viz, (i) no switching, (ii)probes A and B switched, (iii) probes B and C switched, (iv) probes Cand A switched, (v) probe A on phase C, probe B on phase A, probe C onphase B, and (vi) probe A on phase B, probe B on phase C, probe C onphase A;

calculating resulting power factor angles for all of the phases with thecurrent probes reversed;

of the six cases, selecting two cases which give power factor anglesbetween 0 and 90 degrees for all three phases, using the power factorangles for each phase;

calculating total real power of the motor for each of the two selectedcases; and

recommending the two selected cases along with the values of the totalreal power, power factor angle and RMS current for each of the two casesfor switching correction.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary, as well as the following detailed description ofpreferred embodiments of the invention, will be better understood whenread in conjunction with the appended drawings. For the purpose ofillustrating the invention, there are shown in the drawings embodimentswhich are presently preferred. It should be understood, however, thatthe invention is not limited to the precise arrangements andinstrumentalities shown. In the drawings:

FIG. 1 is a functional schematic block diagram of a preferred embodimentof a system for analysis of a three phase motor in accordance with thepresent invention;

FIG. 2 is a more detailed functional schematic diagram of a portion ofthe system shown in FIG. 1;

FIG. 3 is a flow diagram of a preferred method of calibrating thesensors in accordance with the system of FIG. 1;

FIG. 4 is a flow diagram of a preferred method of determining shaftspeed and slip utilizing the spectra of current traces in accordancewith the system of FIG. 1;

FIG. 5 is a flow diagram of a preferred method of detecting pole passfrequency in accordance with the system of FIG. 1;

FIG. 6 is a flow diagram of a preferred method of determining statorwinding condition in accordance with the system of FIG. 1;

FIG. 7 is a flow diagram of a preferred method of detecting broken rotorbars in accordance with the system of FIG. 1;

FIG. 8 is a flow diagram of a preferred method of measuring motorefficiency in accordance with the system of FIG. 1;

FIG. 9 is a Condition/Performance Report (CPR) display, includingexample values, in accordance with the present invention;

FIG. 10 is a bar diagram for displaying traditional phasor diagraminformation, in accordance with the present invention;

FIG. 11 is a bar diagram for displaying traditional phasor diagraminformation showing motor operation with a lagging or inductive powerfactor of zero, in accordance with the present invention;

FIG. 12 is a bar diagram for displaying traditional phasor diagraminformation showing a synchronous motor at zero leading or capacitantpower factor, in accordance with the present invention;

FIG. 13 is a prior art voltage and current waveform diagram;

FIG. 14 is a prior art phasor diagram displaying the voltage and currentinformation of FIG. 13;

FIG. 15 is a bar diagram in accordance with the present inventiondisplaying the voltage and current information of FIG. 13;

FIG. 16 is prior art phasor diagram illustrating voltage and currentinformation where A and B current probes are switched;

FIG. 17 is a bar diagram in accordance with the present inventiondisplaying the voltage and current information of FIG. 16;

FIG. 18 is prior art phasor diagram illustrating normal phasors with thedirection sense of the B current probe being wrong;

FIG. 19 is a bar diagram in accordance with the present inventiondisplaying the voltage and current information of FIG. 18;

FIG. 20 is prior art phasor diagram illustrating a situation where theA, B and C current probes are reversed in orientation; and

FIG. 21 is a bar diagram in accordance with the present inventiondisplaying the voltage and current information of FIG. 20.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is directed to an apparatus and method ofcomprehensively evaluating the condition and performance of inductionmotors, particularly three-phase induction motors, through the use of amotor monitor. The motor monitor can be linked to a processor executinganalysis and database software for storing motor data and analyzing andreporting on the condition of the motor. The motor monitor can beconnected to the processor through a variety of means, including bothhard-wired means and non-hardwired means, such as by infrared or otherwireless transmission.

Referring to the drawings, wherein the same reference numerals indicatelike elements throughout the several figures, there is shown in FIG. 1 afunctional schematic block diagram of a preferred embodiment of aprocessor-based motor monitor system 10 which operates in accordancewith the methods of the present invention. In the presently preferredembodiment, the system 10 includes a processor 12 which preferably is acommercial microprocessor, such as an Intel x86 type processor orsimilar processor, although other processors may also be used with thepresent invention, such as a digital signal processor, as are known tothose of ordinary skill in the art of data collection devices.Preferably the processor 12 includes or has access to a memory, whichpreferably includes a read only memory (ROM) 14 employed for storingfixed information, such as executable processor code and/or fixed dataparameters or parameter ranges, and a random access memory (RAM) 16 of apredetermined size which is adapted for temporary storage of dataaccumulated for analysis. The ROM 14 is of a type well known to those ofskill in the art for storing fixed information or information which isnot changed by the processor 12 during execution of processoroperations. However, the ROM 14 may be of the type which can bereprogrammed (e.g., a PROM, EPROM, EEPROM, etc.) or otherwise changedperiodically to update, modify or change how the processor 12 operates.The RAM 16 may also be used for temporarily storing portions of theexecutable code or input information. As will also be known to those ofordinary skill in the art, other memory devices could also be connectedto the processor 12, such as a magnetic or optical storage device, or aPCMCIA compatible storage device (not shown) for storing collectedand/or processed data and related information, such as a time stamp.

A keypad 18 is presently employed as the primary user input device topermit a user to communicate with the processor 12. The keypad 18includes a plurality of buttons or switches for inputting information orcommands. In the presently preferred embodiment, the keypad 18 includesbuttons for instructing the system 10 to display previously recorded orstored data, including power data and motor condition flag histories fordesignated time periods, power quality data, such as per phase voltageand current data, and power conversion data, such as input power, outputpower and motor speed. The keypad 18 also preferably includes one ormore buttons related to motor identification information. Although akeypad 18 is presently preferred, it will be appreciated by thoseskilled in the art that any other type of input device may be employedinstead of or in addition to the keypad 18, such as a keyboard, mouse ortrack ball type device which allows a user to scroll throughpredetermined command screens, as is known in the art.

A display 20 is connected to the processor 12 for displaying output fromthe processor 12. The display 20 provides information to a user, such asthe per phase voltage and current data, power data and motoridentification information, as well as event flag information foralerting the user of a potential problem with the motor system, such asa problem with the motor rotor, the stator, current, voltage,performance, or loading. In the presently preferred embodiment, thedisplay 20 comprises a four line LCD display in combination with anarray of LEDs. The LCD display displays motor data, as previouslydiscussed, such as per phase current and voltage data and powerinformation and the LEDs display event flags for alerting the user topotential motor problems. Of course, other types of suitable outputdevices may be employed in addition to or instead of the display 20,such as a CRT, a VDT, or a printer. In addition to the display 20, aremote display (not shown) may be included which is located at a motorcontrol center (MCC) so that an operator or technician is not requiredto leave the MCC to check on the condition of a motor. Alternatively,the display 20 could be located remotely from the motor, such as at theMCC.

The processor 12 further includes at least one communication port 22which may be either a parallel port, a serial port, or both. Thecommunication port 22 is employed for receiving data from anotherlocation or device, for transmitting data to another device or forsending data to another location utilizing a modem or other suchtransmission device (not shown) in a manner well known in the computerart. In the presently preferred embodiment, the communication port 22 isused to download stored information, such as information stored in theRAM 16 to another data storage device or a computer, such as a personalcomputer system well known to those skilled in the art. Ultimately, inthe presently preferred embodiment, information stored in the memory(e.g., the RAM 16) is transmitted to a computer (not shown) operatingaccording to the methods of the present invention, which analyzes andprocesses the information. In addition, the processor 12 also includesan input port 24 for receiving sensor data, as described in more detailbelow.

In the presently preferred embodiment, the processor based system 10comprises a relatively small and unobtrusive device for collecting andstoring motor data, which data is then downloaded, transmitted, orotherwise transferred to a computer (not shown), for processing.However, it will be apparent to those of ordinary skill in the art thatthe system 10, as opposed to being a relatively small and unobtrusivedata collection and storage device, could also comprise a moresophisticated device, such as a personal or laptop computer. Also,variations in the input/output components of the system 10 may be madedepending upon particular applications. For example, in someapplications, both a printer and a video display 20 may be desired. Inother applications, a keyboard, as opposed to the small keypad 18 may bedesired. It should, therefore, be clearly understood by those skilled inthe art that the present invention is not limited to the particularhardware configuration shown in FIG. 1 but may be implemented using anytype of hardware configuration suitable for a particular application.The processor based system 10 may comprise a personal computer, or anyother suitable type of computer, such as a lap-top computer,mini-computer, main frame computer or the like.

The above-described system 10 is employed for on-line analysis of theoperation of a polyphase motor driving a load, the polyphase motor beingillustrated schematically as a three-phase motor 30. In the presentlypreferred embodiment, the present invention is directed particularly toanalyzing the performance and condition of a three phase induction motor30 using only three phases of current and voltage. The motor 30 isconnected to a suitable power source 32 utilizing a suitable three-phasecable 34 having individual conductors or supply lines, including ana-phase conductor 34a, a b-phase conductor 34b, a c-phase conductor 34c,and if appropriate, a neutral conductor 34n.

The output of the motor 30 is connected through a suitable output shaftor other type of mechanical transmission means 36 to a load 38 which maybe a fan, pump, compressor, valve or virtually any other type ofmachinery or equipment. Depending upon the application, the transmissionmeans or transmission 36 may include suitable clutches, gearing, beltsor other mechanical interconnecting devices (not shown) of a type wellknown in the art. For the sake of brevity, the combination of the motor30, transmission 36, and the load 38 will herein sometimes becollectively referred to as the motor system. It should be appreciatedby those skilled in the art that the present system 10 may be employedfor analysis of polyphase induction motors which may be connected to anysuitable type of power source 32 for driving any type of load 38 (evenno-load) utilizing any type of transmission means 36, and that theembodiment shown in FIG. 1 is only for the purpose of illustrating apreferred embodiment of the structure and operation of the presentinvention.

The system 10 further includes a plurality of individual sensors orprobes shown collectively as 40, for monitoring predetermined electricaland mechanical variables of the motor 30 and transmission means 36, andfor converting the monitored characteristics into electrical signals forprocessing by the processor 12. In the present embodiment, the sensors40 include three clamp-on current probes 42, 44, 46, one of the currentprobes being clamped to each of the conductors 34a, 34b, 34c, of thethree phase cable 34 interconnecting the motor 30 with the power source32. The clamp-on current probes 42, 44, 46 are generally of a type wellknown in the electrical measurement art and are commercially availablefrom a variety of well known sources. The current probes 42, 44, 46 canbe inductive or Hall effect or any other type which converts current ina conductor into a related voltage signal. The currents may also betransduced by current shunts or by current transformers instead of theclamp-on type of sensors. Additional, optional current sensors (notshown) for detecting ground leaks may be provided for surrounding two ormore phase leads. The probes may be applied to the motor circuitdirectly or to any control circuit which follows the phase currentsproportionally. When current transformers (not shown) are used, thepresent invention corrects or compensates for any amplitude and phaseshifts caused by the transformers, as described in more detail below.Since current probes are known to those of ordinary skill in the art,complete details of the structure and operation of the current probes42, 44, 46 are not necessary for a complete understanding of the presentinvention.

The sensors 40 further include voltage probes 48, 50, 52, each of whichis connected to one of the conductors 34a, 34b, 34c of the three phasecable 34 and, if a neutral conductor 34n, shown in phantom, is present,a fourth voltage probe 54 is connected to the neutral conductor 34n ofthe cable 34. The voltage probes 48, 50, 52, 54 are generally of a typewell known in the art and are commercially available from a variety ofsources. For larger power systems with higher voltages, directconnection of the voltage probes 48, 50, 52 to the individual phaseconductors 34a, 34b, 34c is generally impractical, and thus, potentialtransformers (not shown) may be used which reduce the voltage at themeasurement point. The probes 48, 50, 52 are still used, but areconnected to the output of the respective potential transformer insteadof directly to each of the individual phase conductors 34a, 34b, 34c. Asdiscussed in more detail below, if the voltage probes 48, 50, 52 areconnected to a transformer, then compensation is made, in the presentinvention via software, for any reduction in voltage and any phaseshifts caused by the transformer (for instance, as is known in the art,wye-delta and delta-wye transformers introduce a 30° phase shift). Sincevoltage probes are generally commercially available and known to thoseof skill in the art, further details of the structure and operation ofthe voltage probes 48, 50, 52, 54 are not necessary for a completeunderstanding of the present invention.

In addition to the above-discussed electrical sensors, the presentsystem 12 may include one or more mechanical sensors. The mechanicalsensors may include a vibration sensor 56 which may be an accelerometer,an acoustic sensor 58, and a tachometer 60 providing a once perrevolution phase reference for sensing the rotating speed of the outputshaft of the motor 30 and of the shaft of the load 38 if different dueto an intervening gear box or belt within the transmission 36. One ormore additional mechanical probes may also be provided. Such additionalmechanical probes may include pressure transducers, vibration sensors,temperature probes, proximity probes, force sensors, torque sensors andaccelerometers having different locations or orientations from that ofsensor 56, etc. Each of the mechanical sensors are adapted to receiveand convert sensed mechanical parameters related to the operation of themotor system into analogous standard electrical signals. Details of thestructure and operation of the various mechanical sensors are notnecessary for a complete understanding of the present invention. Itshould be understood by those skilled in the art that while certainmechanical sensors are specifically discussed and illustrated, othermechanical sensors may be employed either in addition to the discussedsensors or as an alternative to the discussed sensors. Thus, the use ofa particular type of mechanical sensors employed in the presentlypreferred embodiment should not be viewed as a limitation upon theinvention.

The system 10 further includes a plurality of signal conditioners 62which are illustrated collectively in FIG. 1. Preferably, a separatesignal conditioner is provided for each of the sensors 40, with therespective output of the sensor 40 being connected directly to the inputof the respective signal conditioner 62. Each of the signal conditioners62 functions in a manner well known in the art to amplify, impedancematch, filter and otherwise standardize and improve the electricaloutput signals received from the sensors 40. Standardization of signalsincludes conversion of currents to a proportional voltage, amplitudescaling and appropriate filtering to limit bandwidth. The precisestructure and operation of each signal conditioner depends upon theparticular type of sensor 40 with which the signal conditioner 62 isemployed. Preferably, each of the signal conditioners 62 also includesan anti-alias low pass filter which functions to improve the integrityof the acquired sensor data by filtering out, prior to digitizing,sensor signal frequencies greater than approximately half of thesampling rate of the digitizer.

The system 10 further includes a plurality of individualanalog-to-digital (A/D) converters 64 shown collectively in FIG. 1. TheA/D converters 64 function in a manner well known in the art to receivethe conditioned and filtered analog output signals from thecorresponding signal conditioner 62 and convert the received analogsignals at a predetermined sampling rate into digital signals (i.e., astream or array of digital data) for data manipulation and analysis bythe processor 12. A typical sampling rate could be 1,000 samples persecond for each signal. Thus, each of the A/D converters 64 produces anoutput data array or bit stream corresponding to the particular sensor40 with which the analog-to-digital converter is associated.

The outputs of each of the A/D converters 64 are provided to the inputof a multiplexer 66. The multiplexer 66 which, in the present embodimentis preferably a time division multiplexer, receives the digital datasignals from each of the A/D converters 64 and in a manner well known inthe art transmits the received digital data signals to an appropriateserial input port 24 of the processor 12 in a predetermined time spacedorder. It will be appreciated by those skilled in the art that thesignal conditioners 62, A/D converters 64, and multiplexer 66 which areemployed in connection with the presently preferred embodiment, are eachof a type well known in the art and available from a variety ofmanufacturers. Complete details of the structure and operation of thesignal conditioners 62, A/D converters 64, and multiplexer 66 aregenerally well known and need not be described in greater detail herein.Suffice it to say that the signal conditioners 62, A/D converters 64,and multiplexer 66 cooperate to take the raw analog output electricalsignals from the electrical and mechanical sensors 40 and convert theraw signals into a digital form suitable for processing by the processor12. It will be appreciated that the functions of the signal conditioners62, A/D converters 64, and multiplexer 66 may be combined into a singlesub-assembly or may be performed in any of several different manners.Moreover, the arrangement of the component parts may vary from what isshown in FIG. 1, for instance, the analog signals detected by thesensors 40 could be multiplexed prior to being converted to digitalsignals by the A/D converters 64. Thus, while the preferred embodimentemploys such components, the particular components are not intended tobe a limitation on the present invention.

The processor 12 receives and analyzes the digital signals from the A/Dconverters 64 and stores the digital data signals in the RAM 16. In thepresently preferred embodiment, each of the conditioned and digitizedsignals from each of the three current probes 42, 44, 46, and from thethree voltage probes 48, 50, 52 are individually analyzed and processedby the processor 12. As will be appreciated, the processor 12 operatesin accordance with the processor software, preferably stored in the ROM14 or otherwise stored and accessible for execution by the processor 12.Alternatively, the present invention may be implemented using othermeans, such as hard-wired logic circuits (not shown) used in combinationwith or instead of the processor and software.

FIG. 2 shows in greater detail the manner in which the electricalmeasurements are taken. In the illustrated embodiment, both the motor 30and the voltage probes 48, 50, 52 are connected in a wye configuration,with an artificial neutral phase for measuring the phase-to-neutralvoltage. One terminal of each of the voltage probes 48, 50, 52 isphysically connected to each of the individual phase conductors 34a,34b, 34c, respectively, with the other terminals of the voltage probes48, 50, 52 being connected together at point 51 to form an artificialneutral. An optional neutral connection line (N) shown in phantom may beconnected to the neutral of the motor circuit when the motor circuit isaccessible.

The input wye circuit provides the capability to analyze both three andfour wire wye motor configurations. When no external neutral (n)connection is made, the common "star point", indicated at 51, of the3-wire wye circuit is driven to the algebraic mean of the three voltageinputs V_(a), V_(b), and V_(c). That is, the star point 51 automaticallyassumes the "pseudo-neutral" potential (proper neutral for a balancedsystem). This allows the wye circuit to function as a "line-to-line tophase-to-neutral converter". The wye configuration has been found towork well, and is preferred, for 3-wire wye, 4-wire wye, and deltaconfigured motors. In the delta and 3-wire wye configured cases, theneutral (N) is not connected. Although for delta and 3-wire wyeconfigured motors measured with a wye apparatus the individualphase-to-neutral values are artificial, the individual current andline-to-line voltage measurements are accurate, as are the total real,reactive, and apparent powers, and total power factor, and allmeasurements based on these measurements. In the case of a motorconfigured as a 4-wire wye, if the neutral (N) is connected as shown inFIG. 2, all measurements are accurate, including phase-to-neutralmeasurements. It should be understood that while the voltage probes 48,50, 52 illustrated in the present embodiment are preferably connected ina wye configuration, other connections, such as a delta type connectionmay be used.

FIGS. 3-8 are general flow diagrams of methods of the present invention,which methods are readily implemented in software which may be executedby the processor 12 or which may be executed on a computer, such as apersonal computer, to which the data collected by the sensors 40 andstored in the system memory has been transferred. In the presentlypreferred embodiment, the processor based system 10 collects and storesthe data collected by the sensors 40. The collected and stored data isthen down loaded to a computer loaded with software implementing thedata analysis methods of the present invention for providing analysis ofthe operation of the polyphase motor 30, its transmission 36, and itsload 38 (i.e., the motor system). The computer manipulates the sampleddigital data received from the electrical and mechanical sensors 40 in amanner hereinafter described and generates highly accurate outputs inthe form of discrete data or plots of data versus time (traces)corresponding to particular electrical and mechanical parameters fromwhich specific problems and faults can be identified. In addition, thepresent invention automatically detects such faults and indicates sameto the user in high-level text messages, such as "stator winding fault".Only the particular identified problem(s) need then be repaired, be iton the motor 30, transmission 36, or load 38, thereby saving the cost ofa complete motor system overhaul. Although the steps in the flowdiagrams are shown as being executed sequentially, it will be understoodby those of ordinary skill in the art that at least some and possiblymany of the steps may be implemented in parallel and are not necessarilydependent upon the prior step shown in the flow diagram being executedfirst. Accordingly, the present invention is not meant to be limited toperforming each of the steps shown in the exact sequence shown.

As previously discussed, the sensors 40 and related hardware (signalconditioners 62 and A/D converters 64) often introduce phase shifts ortime delays between the data signals of each of the individual phaseconductors 34a, 34b, 34c. In the present invention, the phaserelationship between each of the conductors or supply lines 34a, 34b,34c is important, and thus the present invention compensates for suchphase shifts introduced into the digital data signals without the use ofany added hardware, such as a phase meter.

Referring now to FIG. 3, the manner in which such phase shifts or timedelays introduced into the digital data signals is compensated for isshown beginning at block 70, by calibrating the probes 42-52 and theassociated signal conditioners 62 and determining a phase deviation foreach of the digital data signals associated with each of the phaseconductors 34a, 34b, 34c. Compensation for system errors is importantbecause it is desirable to measure current and voltage phases veryaccurately in order to accurately determine power factor and power(real, reactive and apparent) for the polyphase motor 30. First, at step72, the three current probes 42, 44, 46 and the three voltage probes 48,50, 52 are placed on a single-phase lead (i.e., one of 34a, 34b or 34c)of known power factor from which the actual phase difference between thevoltage and current can be computed. The power factor of the selectedphase lead is determined using a calibrating instrument to provide asingle phase current which is either in phase with the voltage or at aknown out-of-phase relationship to the voltage. Alternatively, the powerfactor of the selected phase lead may be determined using an arbitrarybut stable circuit having voltage and current measured using the sensors42-52, and having a power factor or power factor angle which may beverified using either a calibrated phase meter or power factor meter(not shown).

The phase of each data signal (from each probe or channel) is thendemodulated by means of any standard demodulation technique at step 74by the processor 12. The preferred demodulation technique is tocalculate the Fast Fourier Transform (FFT) of the data signal, zero theDC component, folding frequency and negative frequencies, double thepositive frequencies, and then perform an inverse FFT. The phase is thefour quadrant arctangent (usually known as atan2) of the imaginarycomponent divided by the real component. Then the phase is unwrapped (itis preferred not to use a modulo-2 pi phase representation). All of theFFTs (of the different probe signals) are taken over the same timeinterval. At step 76, one probe signal is selected as a reference andthen at step 78, the reference signal value is subtracted from all ofthe other probe data signals. Finally, in step 80, the phase deviationfor each of the probes is stored (a value of zero is stored for theprobe selected as the reference) in memory, such as the RAM 16. As aresult of this process, the reference signal is at zero degrees, and theother probe data signals are referred to in relation to the referencesignal.

The signal conditioners 62 can be phase-calibrated with the sensors 40or separately, as desired. That is, the phase shift produced solely bythe signal conditioner 62 is measured and compensated by itself(separate from the associated sensor) or a single phase shiftmeasurement and correction is made for the each sensor 42-52 and itsassociated signal conditioner 62 as a unit. Once the phase deviationassociated with each sensor 42-52 is determined (with respect to thereference sensor), the phase is corrected in subsequent calculations bysubtracting a phase offset (i.e., the phase deviation) from the measuredvalue. In this manner, all of the sensors 42-52 are brought into phasealignment so that any phase differences subsequently measured can beattributed strictly to motor and source characteristics.

When sensors are employed in which the phase shift or sensitivity is afunction of frequency or current amplitude, this effect is compensatedfor by either determining the functional relationship between thedependent and independent parameter (for example, effect of frequency,the independent parameter, on-phase shift, the dependent parameter) andadjusting the phase values in accordance with measured line frequency orby creating a table relating the correction to the independentparameter, and looking up the appropriate correction for each case ofthe independent parameter in the table (e.g., a look-up table stored inmemory such as the RAM 16).

In order to calculate shaft speed and motor slip, the present inventionanalyzes spectral signatures of raw current data, received from thecurrent sensors 42-46. For verification, both the shaft frequency andthe pole-pass frequency are identified and used to calculate the shaftspeed. The shaft frequency and the pole-pass frequency show up assidebands around the line frequency on raw current data. The shaftfrequency sidebands occur at f_(line) ±(1-slip)f_(synch) and thepole-pass frequency sidebands occur at f_(line) ±(2·slip)f_(line) ;where f_(synch) is the synchronous frequency equal to 2·f_(line) /numberof poles and f_(line) is the line frequency, which is the dominant peakin the spectrum. In the case of the shaft frequency, the upper sidebandis used to calculate shaft speed and in the case of pole-pass frequency,the lower sideband is used to calculate shaft speed, since the lowersideband is expected to have a larger amplitude than the upper sideband.After identifying the pole-pass sideband and the shaft sidebandfrequency peaks, their amplitudes are compared and the peak with thelarger amplitude is selected for shaft speed calculation.

An alternative method of determining shaft speed is to use demodulatedcurrent signals to calculate the true shaft speed. That is, instead ofanalyzing the raw current signals, a demodulated current signal isanalyzed, as follows: The demodulation process downshifts allfrequencies by the line frequency so that the shaft sideband frequenciesnow show up at the actual shaft frequency, (1-slip) f_(synch), and thepole-pass sideband frequencies show up at the pole-pass frequency,(2-slip) f_(line). The same logic is employed as before, namely, therange (of reasonable occurrence) of shaft frequency is determined andthe highest peak is selected in this range. A reasonable range for theshaft frequency is from 0.9 f_(synch) to f_(synch). The pole-passfrequency can occur from but not including DC in the demodulated signal(actually 4 Δf, where Δf is the frequency resolution of the FFT, for aKaiser-Bessel window) to 0.2 f_(line). The logic of checking foroutliers among the phases, averaging the results and selecting the finalvalues is the same as for the demodulated case.

Referring now to FIG. 4, a flow diagram of a preferred method ofdetermining shaft frequency is shown. It will be understood by those ofordinary skill in the art that program flow diagrams or charts canrepresent various degrees of program operational details, ranging fromhigh-level flow diagrams which show the principles embodied by theprogram to low-level flow diagrams which detail each step of the programoperation. FIG. 4 is a high-level flow diagram. However, it will beunderstood by those of skill in the art from this disclosure that acomputer program can be written which embodies the principles set forthby this disclosure. Further, the preferred embodiment of the inventiondisclosed herein is described with reference to specific values ornumbers of time samples, etc., such as a sampling rate of 1000 samplesper second (sps). It should be understood that such values are providedfor the sake of example only and are not meant to limit the invention,as the specific values are not critical. The values may vary and areadjusted for various applications. For example, 32,768 samples at 1000sps is used because it provides a reasonable bandwidth, a sufficientlylong time record for adequate frequency resolution and because a powerof two lends itself to rapid calculation using the Cooley-Tukey FFTalgorithm (discussed below).

The shaft frequency detection routine of FIG. 4 is shown beginning atblock 82. As previously discussed, the present invention analyzesspectral signatures of raw current data to calculate shaft speed anduses the shaft sideband frequency and the pole-pass sideband frequencyfor verification. First, at step 84, the predetermined range of speedindicating frequencies narrows down the range of the spectrum that mustbe examined for shaft frequency, by estimating the range of the shaftsideband frequency to be from (0.9·f_(synch) +f_(line)) up to but notincluding (f_(synch) +f_(line)). Spectral analysis is conducted at step86 on the current data obtained from the current probes 42-46 byexamining, for example, 32.768 seconds of current data. First, the DCcomponent of the current signal is subtracted out. The DC component iscalculated as the average value of the current signal over the 32,768points. Then, a 32,768 point window, such as the Kaiser-Bessel, isapplied to the current signal by multiplying the 32,768 point currentsignal by an equal length standard FFT window, such as the Hanning orKaiser-Bessel. The Kaiser-Bessel window is preferred because it providessuperior selectivity in the frequency domain. The FFT is calculatedusing a standard Cooley-Tukey algorithm and dividing the resultingspectra by N, where N is the number of points. Adjustments are then madeto the amplitude to compensate for window effects. Finally, a one-sidedspectrum is calculated by eliminating the negative AC frequencycomponents, doubling all of the remaining (positive) AC components andselecting the spectral lines from DC to the folding frequency (halfsampling rate). The Cooley-Tukey power of two FFT is preferred becauseof its speed. However, any FFT, such as the N-point algorithm, may beused. The preferred FFT algorithm should not be limiting. Also, theone-sided spectrum is convenient to work with and is preferred, butagain is not meant to be limiting.

In step 88, the highest spectral peak is identified using the currentsensor data, and all peaks within 12 dB of the highest peak areidentified as candidate peaks. Broad peaks are eliminated by requiringthat for the first three frequency intervals on each side of a candidatepeak, one of the intervals must show a 12 Db drop in amplitude (i.e.,there must be significant roll-off from the local maxima). In addition,the line frequency peak and glitches are eliminated from considerationby requiring that the first three frequency lines on each side of acandidate peak be monotonically decreasing in magnitude. Afterelimination of false peaks, the highest peak in the range of interest isselected for each of the three spectra (i.e., I_(a), I_(b), I_(c)).

Step 90 is an alternate way of eliminating broad peaks. Step 90 measuresthe RMS noise level to determine a noise floor in the spectra and screenout non-discrete peaks using the current spectra and the list ofcandidate peaks, by measuring the RMS noise level of the spectrum rangeand deleting spectral components within ±0.3 Hz of the peaks. Inaddition, any peaks whose amplitude at a point halfway to the noisefloor is greater than the FFT window roll-off plus a tolerance for noiseare eliminated, in order to eliminate nondiscrete signals.

In step 92, the best shaft frequency peak in each of the three spectrais selected as the maximum amplitude of each of the peaks remainingafter step 90. In step 94, the precise parameters of each of the threepeaks selected in step 92 are determined by calculating the true peakfrequency and the magnitude of each of the three peaks by applyingpicket fence corrections for the Kaiser-Bessel window. For isolatedpeaks well above the noise level, this identifies the parameters withhigh accuracy.

For the Hanning window, the picket fence corrections are given as:##EQU1## where ΔdB=amplitude difference between the two highest linesaround the peak; ##EQU2##

For a Kaiser-Bessel window, the picket fence corrections are calculatedas follows: (a) applying the Kaiser-Bessel window to the data; (b)calculating a one-sided FFT of the weighted data (in dB); (c) locatingthe highest peak in the specified range and finding the frequency andamplitude corresponding to that peak (denoted as est₋₋ freq and est₋₋amp respectively). If two peaks of the same amplitude are found, then:true signal frequency=frequency corresponding to left peak+del₋₋ f/2;true peak=amplitude of left peak+1.0175131556 (dB); (d) checking theamplitudes of the closest spectral lines on both sides of the highestpeak, wherein if the line on the left of the highest peak is higher thanthe line on the right, then flag=-1, and if the line to the right of thepeak is higher than the line to the left of the peak, then flag=+1, andif both the line on the left of the peak and the line on the right ofthe peak are equal, then no corrections are required; (e) calculatingdel₋₋ db=amplitude of highest peak--amplitude of next highest peak(del₋₋ db is always positive); (f) calculating

    del.sub.-- fc=((-0.120583213·del.sub.-- db)+0.498649196)·del.sub.-- f

del₋₋ f=frequency resolution of the FFT and del₋₋ fc is between 0 anddel₋₋ f/2; (g) calculating the signal frequency (cal₋₋ freq) as:

if flag=+1; cal₋₋ freq=est₋₋ freq+del₋₋ fc;

if flag=-1; cal₋₋ freq=est₋₋ freq-del₋₋ fc;

(h) calculating

    del.sub.-- L=((-0.060538416·del.sub.-- db.sup.2)+(0.495432455·del.sub.-- db)+1.01575381)

(del₋₋ L is always positive); and

(i) calculating the true peak as: est₋₋ amp+del₋₋ L.

Finally, in step 96, a best estimate of true shaft speed is determinedusing all available information and weighting the influence of each bitof information by the strength of the signal. However, prior toperforming a weighted average calculation, in order to preventextraneous signal values (i.e., an outlier) from corrupting theaveraging process, any of the three peaks that is not within (equal toor less than) 0.1 Hz of the other peaks (nonlinear filtering) iseliminated. If no peaks are found to be within 0.1 Hz of each other,then a message is sent to the user that the speed cannot be determinedand the program then allows the user the option of estimating the speed(in RPM). If there are peaks found within 0.1 Hz of each other, then, ofthe three (or fewer) remaining peaks, an average is calculated weightedby the energy (magnitude squared) of each peak. The shaft frequency isthen calculated by subtracting the line frequency from the average.

If there are serious interfering tones (i.e., tones of approximately thesame amplitude as the shaft frequency tones) in the spectrum whichprevent confident detection of shaft frequency, the calculation isimproved by demodulating the raw current signals, calculating themagnitude of the demodulated current signals, calculating a spectrum foreach electrical phase, and then using the complex results to calculatethe zero sequence spectrum which detects the diagnostic tones andattenuates the interfering tones.

Referring now to FIG. 5 a flow diagram of a preferred method ofdetermining pole pass sideband frequency in accordance with the presentinvention is shown, beginning at step 98. The procedure for determiningpole pass sideband frequency is similar to the aforedescribed procedurefor determining the shaft sideband frequency. The range of the spectrumthat is examined for pole-pass frequency is: 0.8·f_(line) to (f_(line)-4·Δf), where Δf is the resolution of the FFT (Δf=1/32.738). A 4-Δffactor is used to account for rolloff of the Kaiser-Bessel window, whichin the worst case (when a true peak is at the center of 2 spectrallines) spans ˜4 spectral lines on either side of the true peak. This4-Δf factor imposes a lower bound on the slip value (i.e., slip valuebelow which the pole-pass frequency cannot be identified). ForΔf=1/32.768, slip must be greater than (4·Δf)/(2·f_(line) =˜0.1% for 60Hz line frequency. Although 4·Δ is preferred, 5·Δ can be used for addedsafety.

At decision block 100, before calculating the pole pass sidebandfrequency, the number of poles is determined. If the number of poles isunknown, it is calculated for induction motors by the steps of: (a)dividing the line frequency by the nominal or approximate or nameplateshaft frequency, using the same units; (b) rounding to the next lowerinteger; and (c) multiplying by two. If the number of poles is two,program execution proceeds with step 102. If the number of poles is 4, 6or 8, then execution proceeds with step 104. If there are ten or morepoles, then execution proceeds with step 106.

In the case of two pole motors, the synchronous frequency is equal tothe line frequency. This implies that at very low loads/slip values, itis difficult to detect the shaft frequency because of its proximity tothe second harmonic of the fundamental frequency. The lower limit on theslip, in case of a 32,768 point FFT, is (4/32.768)/f_(synch) =0.2% for a60 Hz line frequency, whereas for a 65,536 point FFT, the lower bound onthe slip is (4/65.536)/f_(synch) =0.1% for a 60 Hz line frequency.Accordingly, it is presently preferred to use an increased dataacquisition period (at least 65.536 seconds) at step 108.

At step 110, the shaft sideband frequency search range is calculated as1.9·f_(line) to (2·f_(line) -4·Δf), where Δf=1/65.356. This search rangeavoids the second harmonic being mistaken as the shaft sidebandfrequency peak. For pole-pass sideband frequency detection the lowerbound equals (4/65.536)/(2·f_(line))=0.005%. The pole pass sidebandfrequency is then calculated using the steps outlined in FIG. 4 fordetermining shaft sideband frequency, beginning with step 86.

At step 104, if the number of poles is four, six, or eight, then theprocedure outlined in FIG. 4 for determining shaft sideband frequency isused, beginning with step 86. At step 106, for motors with 10 poles (ormore), the range of the lower sideband shaft frequency is a subset ofthe estimated pole-pass sideband frequency range (lower sideband). Whenthe shaft sideband frequency peak has a larger amplitude than thepole-pass sideband frequency peak (usually in case of motors withoutrotor faults), this can result in the shaft sideband frequency peakbeing wrongly identified as the pole-pass sideband frequency peak.Therefore, for motors with 10 (or more) poles, it is important that theupper sideband shaft frequency peak is identified first (as is the usualcase), at step 112. The upper sideband shaft frequency peak isidentified as the highest peak in the predefined range (f_(line)+(1-slip)f_(synch)). Then, the corresponding lower sideband iseliminated from the pole-pass frequency search range at step 114 byeliminating ±4 spectral lines about the lower sideband shaft frequency.Note that this is not necessary for fewer than 10 pole motors. Aftereliminating the lower sideband, the procedure outlined in FIG. 4 fordetermining shaft sideband frequency is used, beginning with step 86.

The above procedure does not work when the pole-pass sideband frequencypeak has a larger amplitude than the shaft sideband frequency peak, dueto broken rotor bars or otherwise, and the loading on the motor 30 issuch that the pole-pass sideband frequency peak is located in the shaftsideband frequency range. Such conditions result in the shaft sidebandfrequency peak and the pole-pass sideband frequency peak being mistakenfor each other, though the range of slip (load) over which this ispossible is very small. For example, for a 10-pole motor with apole-pass sideband frequency peak with a larger amplitude than the shaftsideband frequency peak, the slip range which may create problems is9%-10%; for a 22-pole motor with a pole-pass sideband frequency peakwith a larger amplitude than the shaft sideband frequency peak, the sliprange which may create problems is 4.09%-4.55%.

In the case of the pole-pass sideband frequency being identified as theshaft speed indicator, slip is calculated first, then the shaft speed iscalculated. Slip is an important parameter when calculating efficiency.Slip is calculated from synchronous speed and shaft speed and isexpressed as a percentage, as follows: Slip (%)=(synchronous speed-shaftspeed)*100/synchronous speed.

Referring now to FIG. 6, a flow diagram of a preferred method ofdetermining stator winding condition in accordance with the presentinvention is shown, beginning at step 116. First, at steps 118 to 126,the positive, negative, and zero sequence components are calculatedusing the instantaneous phasors, which are obtained from an analyticsignal representation of the voltage and current signals, from thecurrent and voltage sensors 42-52. At step 118, the instantaneous phaseangles of all phasors (V_(a), V_(b), V_(c), I_(a), I_(b), I_(c)) arereferenced to the phase angle of V_(a). This is done by subtracting theinstantaneous, unwrapped phase of V_(a) from the likewise instantaneous,unwrapped phases of V_(b), V_(c), I_(a), I_(b), and I_(c). V_(a) thenhas a zero phase. The other phasors have non-zero but stable(essentially constant) phases.

At step 120, after each phase has been referenced to V_(a), the phasesof each phasor are averaged, in order to reduce noise and at step 122,the instantaneous RMS values of each phase are averaged. At step 124,using the average RMS and average phase angle values calculated in steps118 to 122, phasors V_(A), V_(B), V_(C), I_(A), I_(B), and I_(C) areformed. At step 126, the zero, positive, and negative sequencecomponents are calculated using the following equations: ##EQU3## wherea=e.sup.∫120°X₀ =zero sequence component

X₁ =positive sequence component

X₂ =negative sequence component

The above formula is valid for motors running in the ABC sequence. Themagnitude of X₁ will always be greater than X₂. If the magnitude of X₁turns out to be less than that of X₂, then the values of X₁ and X₂ areexchanged, and the motor sequence is ACB. Accordingly, at step 128, thevalue of X₁ is compared to the value of X₂. If X₁ is less than X₂, thenstep 130 is executed, which exchanges the values of X₁ and X₂. Afterexchanging the values of X₁ and X₂, execution continues with step 132.In the case of X₁ is not less than X₂, then execution proceeds from step128 directly to step 132, without executing step 130. It is recognizedthat alternative methods of calculating the negative sequence componentscan be performed. In the above process, the normal electrical phasorswere averaged before transformation to symmetrical components (i.e.,zero, positive and negative sequence components). Alternatively, thetransformation can be done first on an instantaneous basis so theelectrical waveforms are represented as symmetrical component waveforms,which are phase-referenced to one component, and averaged as symmetricalcomponents. In other words, the electrical components can be averagedbefore or after the symmetrical transformation. Also, it should berecognized that there are other mathematical expressions (such as usingindividual equations instead of a matrix equation) of the symmetricaltransformation which are mathematically equivalent to the equationabove. Accordingly, the present invention is not meant to be limited tothe preferred method, disclosed above, of calculating the negativesequence component.

At step 132, the ground leakage is calculated. The zero sequence currentrepresents ground leakage because, by Kirchoff's law for currents, thesum of all current paths from a point must be zero. The ground leakageis calculated as the ratio of the zero sequence current RMS to thepositive sequence current RMS: ##EQU4## If the ground leakage % ishigher than the specified threshold then a stator fault is reported. Inthe presently preferred embodiment, the ground leakage threshold is setat 5.0%.

At step 134, the effective negative sequence impedance is calculatedfrom the symmetrical components, according to the following equation:##EQU5##

At step 136, winding fault indicators are determined. The most fruitfulway of analyzing the data is to look at both the magnitude and phase (orequivalently, the real and imaginary parts) of the negative sequenceimpedance because the real and imaginary components of the effectiveimpedance change in the event of a fault, sometimes oppositely andsometimes together. To catch all possible occurrences, the negativesequence reactance (X₂) and the negative sequence resistance (R₂) areused, which are referenced to the baseline normal situation for themotor 30:

    ΔX.sub.2 =X.sub.2,new -X.sub.2,baseline

    ΔR.sub.2 =R.sub.2,new -R.sub.2,baseline

At step 138, winding unbalance is calculated, based on currentunbalance, as: Current unbalance--Voltage unbalance, where voltageunbalance is calculated as the maximum deviation from the mean dividedby the mean multiplied by 100 and current unbalance is similarlycalculated as the maximum deviation from the mean divided by the meanmultiplied by 100. If the calculated winding unbalance is higher than aparticular threshold, then a stator fault is reported. In the presentlypreferred embodiment, if the calculated winding unbalance is greaterthan approximately 3.0%, than a stator fault is reported. Although avalue of 3.0% is specified, an alternative method of establishingthresholds, as opposed to or in addition to using a preestablishedvalue, is to monitor the motor system 30 for a period of time and thensetting thresholds based on standard deviation calculations fordetermining faults.

Unbalance may also be calculated by other methods, such as taking theratio of the negative sequence to the positive sequence components (andexpressing as a percent if desired), and by the difference between thehighest and lowest RMS values, divided by the mean RMS value (andmultiplied by 100 if desired to be expressed as a percentage).

At step 140, if either of the thresholds identified in steps 136 or 138was exceeded, a stator fault condition is indicated and the phase inwhich the stator fault has occurred is determined by calculating thereal power in each of the three phases, identifying the two phases withthe highest real power consumption, and then identifying the "faulty"phase according to the logic shown in TABLE 1. The real power for eachphase is calculated as the RMS current multiplied by the RMS voltage foreach phase, multiplied by the power factor, respectively. Note that thesequence (ABC or ACB) was previously determined at step 128.

                  TABLE 1                                                         ______________________________________                                        2 PHASES WITH HIGHEST                                                                          PHASE WITH STATOR FAULTS                                     REAL POWER       Sequence ABC                                                                              Sequence ACB                                     ______________________________________                                        A & B            B           A                                                B & C            C           B                                                A & C            A           C                                                ______________________________________                                    

Referring now to FIG. 7, broken rotor bars are detected according to theroutine beginning at step 142, in the following manner. A broken rotorbar generally results in a reduction in torque in every rotation and hasa corresponding effect on each of the three electrical phases. Morespecifically, the three phases cause three magnetic fields to rotatearound at synchronous speed. The rotor rotates around more slowly,differing in speed by a slip frequency. Since each rotor bar rotatesthrough each magnetic field twice, a broken rotor bar (which causes lessback EMF than a non-broken rotor bar) effects each phase current at twotimes the slip frequency. The present state of the art is to examine thespectrum of the current in one phase for side bands separated from theline frequency by two times the slip frequency, and then determining ifthe amplitude is within approximately 45 dB of the amplitude of the linefrequency component. If so, this indicates the presence of one or morebroken rotor bars.

At step 144, current I_(a) data is sampled, using current probe 42, fora predetermined time period, for instance, 16.384 seconds or 32.768seconds. At step 146, the DC component of the current signal issubtracted out of the data sample. The DC is calculated as the averagevalue of the signal over the 32,768 points. Then, a 32,768 point windowis applied by multiplying the 32,768 point signal by an equal lengthstandard FFT window, such as the Hanning or preferably, theKaiser-Bessel. At step 148, a one sided FFT is calculated. In thepresently preferred embodiment, the standard Cooley-Tukey algorithm isused to calculate the one sided FFT and the resulting spectra is dividedby N (the number of points). Note that this is the same algorithm asused in step 86 (FIG. 4) in determining shaft frequency.

At step 150, the broken rotor bar frequency is calculated as:

    f.sub.BRB =f.sub.line -2·s·f.sub.line

f_(BRB) =broken rotor bar frequency, which is the lower twice-slipsideband around line frequency; s is the calculated value of slip. Sincethe FFT is calculated at discrete frequencies, in general, there is anerror in both the amplitude and frequency of the highest line in thefrequency spectrum. These errors depend on the type of FFT window used(i.e., Hanning or Kaiser-Bessel). The corrections used to compensate forthese errors are called picket fence corrections. Accordingly, toprecisely calculate the magnitude of the broken rotor bar frequencycomponent, a picket fence is applied. The picket fence is modified tolook within ±1 spectral line of an estimated peak placement so as not tobe interfered with by a strong neighboring synchronous component. Then,the magnitude of the pole-pass sideband is divided by the magnitude ofline frequency.

At step 152, apply the following formula to convert to dB: ##EQU6## Atstep 154, a comparison is made to a predetermined threshold, in thepresently preferred embodiment 45 dB. If the absolute dB value isgreater than or equal to the threshold then the rotor is normal, whichis reported to the user at step 156. However, if the absolute dB valueis less than the threshold, execution proceeds to step 158 to examinethe fifth harmonic sidebands. Sidebands around the fundamental frequencycan have significant amplitude because of belt transmission and air gapasymmetries, as well as broken rotor bars. Thus the indicator issupplemented by fifth harmonic information. At step 158, the peaks (±1spectral line) around the following frequencies: f_(line) (5-2·s)f_(line) (5-4·s) and f_(line) (5-6·s) are located. A picket fence isused to calculate the true peak amplitudes and then find the highestpeak of the three currents. If the highest peak is within 14 dB of orgreater than the fifth harmonic, then the rotor condition is not normaland broken rotor bars are reported to the user at step 160. Typically,within 14 dB indicates broken rotor bars, although this threshold mayvary with the type of motor. The threshold may also vary with motorload. Otherwise, there is only a possible problem with the rotor, whichis reported to the user at step 160, along with a message giving theuser an option to initiate trending. Alternately, the fifth harmonicsideband can be used as the primary detector of broken rotor bars.

The present invention also uses the data signals collected by thecurrent and voltage sensors 42-52 to determine motor efficiency. Thepresent invention compensates for different power sources used forcoupled and uncoupled tests by incorporating source unbalance and I² Rline loss ("LineLoss") in its calculations. LineLoss is defined as theI² R loss in the line from the measurement point (typically a motorcontrol center) to the motor 30: ##EQU7## where division by 1000converts Watts to KW. Note, RL_(a), RL_(b), and RL_(c) are individualline resistances, as calculated at step 166. When measurements are takenat the motor, LineLoss is not included in the calculations.

Referring now to FIG. 8, a method of determining motor efficiency isshown, beginning at step 162, using average phasor RMS values of currentand voltage. The first step, indicated at 164, is to calculateindividual phase resistances Rs_(a), Rs_(b), Rs_(c) from lead to leadmeasurements by solving the system: Rs_(a) +Rs_(b) =Rs_(a) ; Rs_(b)+Rs_(c) =Rs_(bc) ; and Rs_(c) +Rs_(a) =Rs_(ca), for the uncoupled andcoupled cases. The resistances should be measured as close as possibleto the temperature at which the other measurements are made. Similarly,at step 166, the individual line resistances, RL_(a), RL_(b), RL_(c) arealso calculated. At step 168, the uncoupled loss is calculated as:##EQU8## where "un" denotes uncoupled values and P_(un) is the totalreal power dissipated when the motor is running in the uncoupledcondition. Note that all terms are in the same units of KW. P_(neg) isindicative of the power loss due to source unbalance and is calculatedas the negative sequence power: ##EQU9## whereθ_(V).sbsb.A2,θ_(I).sbsb.A2 are average negative sequence phase values.The values of V and I used in the above calculations correspond to theoperating mode of the motor, i.e., uncoupled or loaded. The negativesequence voltage and current symmetrical components are calculated asfollows: ##EQU10##

At step 170, the core loss (CL) is estimated as percentage, typically60%, of the fixed losses, as follows:

CL=0.6·Uncoupled Loss

At step 172, the stator I² R loss is calculated as: ##EQU11## In thisequation and the No Load Loss equation, the Rs value appropriate to thethermal conditions at the time is used. Further, Rs is measured at themotor 30. If Rs is not measured at the motor 30, then lead resistancemust be compensated for.

At step 174, total real power is calculated as:

    P.sub.i,motor =P.sub.i -LineLoss-P.sub.neg,

where P_(i),motor is the total real power actually dissipated by themotor, P_(i) is the Total Real Power measured at that load. At step 176,the rotor I² R loss is calculated as: rotor I² R loss=(P_(i),motor-stator I² R loss-CL)×s. (Note, s is the previously calculated value ofslip). At step 178, stray load losses are determined in accordance withstandard estimates, as set forth in TABLE 2 (IEEE Standard TestProcedure for Polyphase Induction Motors and Generators, IEEE Std112-1991):

                  TABLE 2                                                         ______________________________________                                        ASSUMED VALUES FOR STRAY LOAD LOSS                                            Machine Rating                                                                              Stray-load loss (% rated output)                                ______________________________________                                        1-125 hp      1.8%                                                            126-500 hp    1.5%                                                            501-2499 hp   1.2%                                                            2500 hp and greater                                                                         0.9%                                                            ______________________________________                                    

For example, for low hp motors, Stray Losses=0.018 (P_(i) -All OtherLosses). Stray Loss=0.018 (P_(i) -Stator Loss-Rotor Loss-Uncoupled Loss)for low hp motors.

At step 180, output power is calculated as: Po=P_(i),motor -uncoupledloss-stator loss-rotor loss-stray loss. At step 182, motor efficiency iscalculated as the ratio of output power to input power: ##EQU12## whichis also expressed as percent by multiplying the above by 100.

Referring now to FIG. 9, a typical display report 184 of the presentinvention is shown. The display report 184 is a Condition/PerformanceReport (CPR) display, including example values. The report 184 can bedisplayed, for instance, on a CRT connected to the processor 12 or on aCRT connected to a computer or processor to which the data collected andstored by the processor 12 has been downloaded. The report details howthe essential condition and performance information can imparted to auser. The CPR display includes important motor diagnostic informationwhich is determined from the data collected by the three current andvoltage sensors 42-52, such as the RMS voltage and the RMS current foreach phase, the mean RMS voltage, the mean RMS current, along with apercent distortion and percent unbalance calculation. CREST is a ratioof the highest peak to RMS, which is indicative of abnormalities in theshape of the waveform. Motor identification information (not shown), isalso included in the report. The CPR display is an example of howessential motor condition and performance information is reported.Typical cases of the condition/performance report are saved so thattrending can be performed, as described in more detail below.

The present invention, via software, reduces the volume of datacollected by the monitor system 10 (or any online motor monitor system),by first categorizing the data by load. In the preferred embodiment thedata is segregated into 5% (of load) intervals. The data within each ofthese intervals is characterized by a small set of parameters: meanvalue, standard deviation, skew, kurtosis, max, min, number ofobservations, and upper and lower confidence limits.

Key statistical information resulting from the above data reductionprocess is saved and trended, i.e., plotted against time, to determinenon-zero slope. While a periodic one-time analysis can detect seriousproblems for a short time span recorded during motor operation,historical trending can provide advanced warning of impending problems.By recording accurate measurements at different times and plotting theresulting records over time or otherwise automatically searching fortrends over time, patterns can be detected that indicate a particularparameter is degrading or changing, indicating an impending faultcondition while the motor is still operating within acceptable limits.Thresholds are established and if a trend develops that either crossesthe threshold or is approaching a threshold, the user is warned of adeveloping problem. By using the techniques of the present invention,motor faults are detected when they are too small to be of concern, andtrended, so that if getting worse, the point at which an operator willwant to take corrective measures can be projected. This allowance forthe preplanning of downtime is one of the essential benefits oftrending. Also, it helps to ensure that the problem will be correctedbefore it becomes an operational problem, shortening motor life andperhaps resulting in catastrophic motor failure. Trending is bestachieved when the data being reviewed is very accurate. The use of theabove-discussed demodulation techniques, correction of phaseinaccuracies, correction of probe non-linearity, etc., of the presentinvention provides a practical way to achieve the required accuracy forproper trend analysis.

Distributions are calculated for a population of each type of motor foreach load interval for which there is enough data to make a meaningfulcomparison. Motors outside of the distribution are identified andhighlighted to warn the user of an anomalous, possibly dangeroussituation.

As previously discussed, the present invention provides a sensormisplacement check of the current probes 42-46 and, if it is determinedthat one or more probes 42-46 are misplaced, the present invention willperform an automatic correction. It is assumed that the voltage probes48-54 are correctly connected. The user can interact and respond tosystem prompts on the display 20 by way of the keypad 18. Initially, theuser is prompted to select a transformer configuration from a list ofpreselected alternatives, such as wye-wye, wye-delta, or delta-wye. Thepresent invention provides a default configuration for the motor 30, sothat the user is not necessarily required to enter any set upinformation. After the three current probes 42-46 and the three voltageprobes 48-52 are connected, a plurality of signal samples are collected,for instance 200 samples from each sensor 42-52. The DC component iseliminated from each data signal and a threshold is defined. In thepreferred embodiment, the threshold is defined by requiring that thepeak voltage and current in any data signal be at least half the peakvoltage or current of the data signal with the greatest peak voltage orcurrent. If the threshold is not met, the system 10 informs the user ofa faulty voltage or current connection, as appropriate. Each of the(six) data signals is then band-limited, demodulated, and a phasor foreach signal is calculated. The signals are bandlimited by a low passfilter and demodulated by performing a time domain Hilbert demodulation.That is, the analytic signal is formed from the original signal as thereal part and the Hilbert transform as the quadrature part. To avoid endeffects resulting from filtering and demodulation, the first and last 50points of the in-phase and quadrature components are eliminated.

The RMS values of all the channels are calculated by calculating theinstantaneous magnitudes for all six channels as: sqrt(in₋₋ phase²+quadrature²), calculating the mean, and multiplying by 1/sqrt(2).Amplitude and phase corrections are then made based on the selectedtransformer. The amplitude correction involves multiplication with ascaling factor, and the phase correction involves addition with aconstant.

The voltage sequence is also checked. In checking the voltage sequence,it is assumed, by default, that the motor 30 is running in the forwardsequence, i.e., ABC. With phase B as the reference, phase A is positive(˜+120°), and phase C must be negative (˜-120°). If this is not thecase, then, the user is alerted by way of a message on the display 20that a reverse sequence has been detected and given the followingoptions: (i) continue, in the case of a reverse direction motor; or (ii)change the voltage probe connections. If the user chooses to change thevoltage probe connections, the processor based system 10 re-checks thesequence.

The system 10 also tests for sensors 42-52 on the same phase. This testcompares the phase angles between the three currents, and between thethree voltages. The test uses the output of the Hilbert phasedemodulation. Whereas the Hilbert routine unambiguously reports thephase angle between -π and π, the calculation of the phase differencesis ambiguous, ranging from -2 π to +2 π. To avoid this ambiguity the Lawof Cosines is applied because it returns the smallest angle between twovectors. Two electrical phases are compared at a time. For example, forcurrent phases A and B, the distance between unit vectors A and B is thesquare root of the sum of the real distance squared and the imaginarydistance squared. The angle ∠AB is then be calculated as: ##EQU13##where a=length of vector A

b=length of vector B

c=distance between vectors A and B

Since A and B are treated as unit vectors, ##EQU14##

The procedure is to: (a) select a pair of voltage or current channels(without mixing voltage and current); (b) calculate the minimumdifference angle for the central 100 (out of 200) points, using theabove formula; (c) calculate the mean of these 100 angles; (d) do so forall three possible voltage pairs and all three current pairs (ab, bc,ca); (e) proceed to test against a threshold. In the presently preferredembodiment, a threshold of 30° is used, although other angles could beused. For example:

    if θ.sub.ia,ib <30° then fail;

Test if ∠V_(a) V_(b) <30°, ∠V_(b) V_(c) <30°, ∠V_(c) V_(a) <30°, and∠i_(a) i_(b) <30°, ∠i_(b) i_(c) <30°, ∠i_(c) i_(a) 30°.

If any angle test fails, then the user is alerted that the two probesinvolved are on the same phase.

Finally, the present invention also tests for switched and reversedprobes. The test for switched and reversed probes also uses the outputof the Hilbert phase demodulation, with the first and last 50 pointseliminated to minimize end effects. Thus, a set of 100 points for eachcurrent and voltage channel is used. First, the difference is takenbetween corresponding current and voltage phase angles at each of the100 points. The difference angle is expressed unambiguously, that is,the angles are expressed in values between -π and π if working inradians or between -180° and 180° if working in degrees. While theHilbert routine returns unambiguous angles, the test creates adifference function, and unless pains are taken, the resulting angle isambiguous.

The switched or reversed probe test first checks that all three (mean)difference angles are between -90 and +90 degrees. In other words, theabsolute (mean) difference angle must be less than or equal to 90°(π/2).The rationale for this test is that the phase difference (power factorangle) between a voltage and its corresponding current cannot be greaterthan 90° for either an induction or synchronous motor (under normaloperating conditions; however, it can momentarily exceed 90° duringlightly loaded startup).

In order to completely avoid ambiguity in specifying the angle, the realand imaginary parts (cos and sine of the difference angle) arecalculated and the test checks the polarity of the mean real component.If the sum or mean of the real values over 100 points is positive, thepolarity is OK for that phase. If negative, then the polarity is wrongand the user is sent a message. By using the real part, the ambiguity ofspecifying the angle is avoided. Symbolically,

if cos (θ_(ia),va)<0 then fail

If the three power factor angles are less than ±90°, then the switchedor reversed probe test next checks to determine if the three (mean)difference angles are within 30° of one another. In symbols: max(difference angle mean)-min (difference angle mean) <=30°. The methodfor detecting if the three mean difference angles (i.e., power factorangles) are within 30°(π/6) of each other is to calculate the differenceangle as the (four quadrant) atan2(imag/real). ##EQU15## There is noambiguity in the angles because the atan2 function reports anglesbetween -π and π (-180° and +180°), and the range is further reduced tobetween -π/2 and π/2(-90° and +90°) because to have gotten this far theconfiguration must have passed the previous 90° test. Thus (max-min)will give a valid measure of the spread of the three phase angles. Astable measure is then determined by taking the atan2 of the sum or meanimaginary over the sum or mean real and checked, as follows: ##EQU16##

The threshold is selected to be 30° because this is half way between theideal case for a balanced system (0°) and the case of switched andreversed probes (60°). Note this 30° test is different than the onewhich tested for probes on the same phase. The present test checks tomake sure the power factor angles on the three electrical phases areapproximately equal. The other 30° test checks to make sure the currentprobe signals are not in phase and that the voltage probe signals arenot in phase. If a failure occurs, then the user is given the followingoptions: (i) physically change the probe connections based on arecommendation by the system 10, (ii) ignore the system warning andproceed, or (iii) allow the system 10, via software, to correct for thewrong probe hook-up.

If the user selects the first option, then a two-step procedure is usedto recommend changes (it is assumed that the three voltage and currentphases are available at this stage). The first step detects whether theprobes 42-46 are switched and recommends the correction, irrespective ofany probe reversals. There are, in all, six possible probe placementcorrections. They are: (i) no switching; (ii) Probes A and B switched;(iii) Probes B and C switched; (iv) Probes C and A switched; (v) Probe Aon phase C, Probe B on phase A, and Probe C on phase B; (vi) Probe A onphase B, Probe B on phase C, and Probe C on phase A. Basically, thesystem 10 checks which of the above six cases of probe placementcorrections gives a reasonable power factor angle for all three phases.

For the purpose of display, the following convention is adopted: theinstantaneous phase angle of each of the six signals is calculated usingvoltage phase B (0°) as a reference. The mean phase angle for eachsignal is calculated with the phase values, for instance, in the 150° to210° range. The phase angles are represented by the following equation:

    if phase>150°, phase=phase -360°;

    if phase<-210°, phase=phase +360°.

For example, if the phase angle is +230°, then 230°-360°=130°; and ifthe phase angle is -170°, then 170°-210°=190°.

A first step, STEP 1, performs the following calculations:

(a) Calculate the resulting power factor angles for each of the probeplacements, denote them as Ang_(x). The power factor angle is calculatedby subtracting the current phase from the voltage phase.

(b) Since probe reversals are also possible, the power factor angles arealso calculated for each case assuming that the probes may be reversed.This is done by simply subtracting 180° from Ang_(x), and denoting themas rev₋₋ Ang_(x).

For example, if the calculated phases from current probes A, B and Care: ph₋₋ I_(a) =50, ph₋₋ I_(b) =-70, ph₋₋ I_(c) =-10, and thecalculated voltage phases are ph₋₋ V_(a) =120, ph₋₋ V_(b) =0, ph₋₋ V_(c)=120, the probe check detects a failure, and when the user selects thefirst option, the

                  TABLE 3                                                         ______________________________________                                        CASE       Ang.sub.a                                                                            r.sub.-- Ang.sub.a                                                                    Ang.sub.b                                                                           r.sub.-- Ang.sub.b                                                                  Ang.sub.c                                                                          r.sub.-- Ang.sub.c                 ______________________________________                                        I.  ph.sub.-- I.sub.a = 50;                                                                  70     -110  70    -110  -110 70                                   ph.sub.-- I.sub.b = -70;                                                      ph.sub.-- I.sub.c = -10;                                                  II. ph.sub.-- I.sub.a = -70;                                                                 190    10    -50   130   -110 70                                   ph.sub.-- I.sub.b = 50;                                                       ph.sub.-- I.sub.c = -10;                                                  III.                                                                              ph.sub.-- I.sub.a = 50;                                                                  70     -110  10    190   -50  130                                  ph.sub.-- I.sub.b = -10;                                                      ph.sub.-- I.sub.c = -70;                                                  IV. ph.sub.-- I.sub.a = -10;                                                                 130    -50   70    -110  190  10                                   ph.sub.-- I.sub.b = -70;                                                      ph.sub.-- I.sub.c = 50;                                                   V.  ph.sub.-- I.sub.a = -10;                                                                 130    -50   -50   130   -50  130                                  ph.sub.-- I.sub.b = 50;                                                       ph.sub.-- I.sub.c = -70;                                                  VI. ph.sub.-- I.sub.a = -70;                                                                 190    10    10    190   190  10                                   ph.sub.-- I.sub.b = -10;                                                      ph.sub.-- I.sub.c = 50;                                                   ______________________________________                                    

(c) Find the (two) cases which give power factor angles between 0 and 90degrees for all the three phases, using either Ang_(x) or rev₋₋ Ang_(x).(In the above example, cases I and VI satisfy this criterion).

(d) Calculate the total real power of the motor 30 for each of the twocases, as:

Total real power=V_(a),rms ·I_(a),rms ·PF_(a) +V_(b),rms ·I_(b),rms·PF_(b) +V_(c),rms ·I_(c),rms ·PF_(c)

Power Factor, Pf_(x) =cos (Pf₋₋ Ang_(x)); where Pf₋₋ Ang_(x) =min [abs(Ang_(x)), abs (rev₋₋ Ang_(x))].

(e) Find the loading condition of the motor for the two cases.

0.7≦Pf_(x) <I highly loaded

0.5≦Pf_(x) <0.7 moderately loaded

0≦Pf_(x) <0.5 lightly loaded

These are default definitions which may be changed or modified by theuser.

(f) The user then has to select between the two cases. The system 10displays (i) the power factor for all three phases, (ii) RMS current,(iii) the total real power and (iv) loading condition of the motor 30,for both the cases.

(g) Recommend appropriate correction based on the selection.

If the user selects case 1, then the present invention informs the userthat the current probes 42-46 are on the right phase, and checks forprobe reversals. The probe check then proceeds to STEP 2. For any othercase, the present invention recommends the respective correction, suchas (case VI): "Place Probe A on phase B, Probe B on phase C, and Probe Con phase A. Do not reverse probes during switching". After thecorrections are made, the probe check proceeds to STEP 2.

In STEP 2, the probe test:

(a) resamples the current signals or re-acquires "fresh" data,demodulates the data, and calculates the voltage and current phasors;

(b) calculates Ang_(x) and re₋₋ Ang_(x) for the three phases;

(c) recommends correction to the user to reverse the phases for whichabs(rev₋₋ Ang_(x))<abs(Ang_(x)).

When the system 10 software makes the changes automatically, STEP 2 isnot performed to detect reversals in the current probes 42-46. Rather,the system software remaps the channels and the reversals are picked updirectly from the above table (TABLE 3). For example, first, data isremapped as: phase B data->probe A; phase C data->probe B; phase Adata->probe C. Then, probes A and C are reversed by inverting the data(multiplication with -1). Note that when remapping is done in thesoftware, calibration data is also carried along with the re-mappings.

The switching and reversing steps are separated when the user makes theprobe corrections because when the probes are switched physically, thereversal of the probe is carried along with the same probe, which is notthe case with remapping the channels (i.e., switching the probes viasoftware). In other words, switching of two probes (with one of themreversed) physically, and switching the phasors in the software does notalways result in the same phase relation between the channels.

Traditional phasor diagrams for displaying per-phase voltage and currentinformation comprises either two overlaid or two separate polar (orvector) representations, one for per-phase voltages and one for theper-phase currents. These polar representations are primarily useful forinstruction. Unfortunately, such polar representations, do not convey anintuitive feel for the state of the motor or of the phase relationshipsbetween the various phase voltages and phase currents in a way that isuseful for monitoring purposes because it is difficult for a user toperceive minor amplitude differences among the three current or voltagevectors at their 120° separation. It is equally difficult to visuallyperceive any small alteration in the 120° angle between similar vectorsand differences among the three power factor angles between the threevoltage and current pairs. Generally, motor faults have to be grossbefore they become visually apparent in the traditional vector diagrams.Accordingly, the present invention presents a new method of displayingper-phase voltage and current information using bar diagrams. The bardiagrams of the present invention generally are easier to interpret thanthe prior art phase diagrams, especially when auditing the installationof probes. Further enhancements to the bar graphs provide additionalvoltage and current information. For instance, making the bars linearover a narrow range around the mean of the currents or voltages permitsenhanced display of voltage and current unbalance and positioning thebars horizontally permits displaying phase relationships. Furtheradvantages will be apparent to those of skill in the art from thedescription which follows:

Referring now to FIG. 13, the current and voltage waveforms for athree-phase induction motor are shown. The voltage waveform 200 includesthe a-phase voltage waveform 202, the b-phase voltage and the c-phasevoltage waveform 206. The current waveform 208 shows the a-phase currentwaveform 210, the b-phase current waveform 212 and the c-phase current214. FIG. 13 shows a simulated measurement from an induction motoroperating at a power factor of 0.85.

FIG. 14 is a prior art phasor diagram showing simulated measurementsfrom an induction motor operating at a power factor of 0.85. The voltagephasor diagram 220 includes the a-phase voltage at 222, the b-phasevoltage at 224 and the c-phase voltage at 226 and the current phasordiagram 230 shows the a-phase current at 232, the b-phase current at 234and the c-phase current at 236.

Referring now to FIG. 15, a bar diagram 240 according to the presentinvention is shown indicating simulated measurements from an inductionmotor operating at a power factor of 0.5. The bar diagram or bar chart240 comprises a horizontal axis 242, a first bar chart 244 for plottingphase-to-neutral voltages which graphically represent phase-to-neutralvoltages of the motor, and a second bar chart 246 for plotting phasecurrents which graphically represent phase currents of the motor. Thefirst bar chart 244 shows the a-phase voltage at 248, the b-phasevoltage at 250 and the c-phase voltage at 252. The second bar chart 246shows the a-phase current at 254, the b-phase current at 256 and thec-phase current at 258. In the preferred embodiment, the voltage barchart 244 is located on a first side of the horizontal axis 242 and thecurrent bar chart 246 is located on a second, opposite side of thehorizontal axis 242. In the presently preferred embodiment, the voltagebar chart 244 is located above the horizontal axis 242 and the currentbar chart 246 is located below the horizontal axis 242 and the voltagebars 248, 250, 252 and the current bars 254, 256, 258 are positionedalong the horizontal axis according to their respective phase angles,such that a power factor angle can be determined directly from thehorizontal axis 242. In FIG. 15, a voltage unbalance of about 2% and acurrent unbalance of approximately 5.5% are shown and are readilydeterminable by viewing the vertical axes 260, 262 of the voltage barchart 244 and the current bar chart 246, respectively. The voltage andcurrent vertical axes, 260, 262 are scaled such that unbalancepercentages are readily determinable. In order to convey such unbalanceinformation on the phasor diagram, FIG. 14, it would requireunconventional (nonlinear) scaling of the vector lengths 222-226 and232-236. In the bar chart 240, the horizontal axis 242 is scaled to showphase relationships between the per-phase voltages and the per-phasecurrents. Thus, it can be seen that each of the per-phase currents asrepresented by bars 254, 256, and 258 trail the per-phase voltagesrepresented by bars 248, 250 and 252, respectively.

Referring now to FIG. 10, a phasor bar diagram 270 in accordance withthe present invention is shown including a horizontal axis 272, avoltage bar chart 274 and a current bar chart 276. The voltage bar chart274 and the current bar chart 276 are shown on opposite sides of thehorizontal axis 272. The voltage bar chars 274 includes three bars, 278,279 and 280 which represent the three-phase voltages of a motor and thecurrent bar chart 276 shows current bars 281, 282 and 283 which displaythe three per-phase currents of the motor. The voltage bar chart 274 isscaled to the average of the three voltages 278, 279, 280 and the bars278, 279 and 280 are drawn to emphasize a range of ±10% of this averagevalue. The current bars 281, 282, and 283 are identically scaled fromthe three per-phase currents. In the presently preferred embodiment,color or texture is used to identify and distinguish the respectivephases (a, b, and c). The bars 278-283 are horizontally positioned inproportion to their phase angles. In the presently preferred embodiment,voltage phase b represented bar 279 is used as a reference and is thuscentered and all other phases are measured from it. In FIG. 10, perfectvoltage and current balances an operation at unity power factor isillustrated. The bars for the a and c phases 278, 280 and 281, 283 are1200 away from those of the b-phase markers 279, 282. The horizontalaxis 272 spans ±210° away from those of the b-phase markers, 279, 282.The horizontal axis 272 spans ±210° from the b-voltage position 279.

Referring now to FIG. 11, a phasor bar chart 290 in accordance with thepresent invention is shown including a voltage bar chart 274, a currentbar chart 276 and a horizontal axis 272. FIG. 11 illustrates operationat a lagging or inductive power factor of 0. Note that the current bars291, 292, 293 are shifted to the right by 90° (the power factor angle).This feature is readily determinable by noting the distance the voltagebars 294, 295, 296 and each of the current bars, 291, 292, and 293,respectively. Note that the current bars 291-293 are shown to the rightof the respective voltage bars 294-296, which indicates that the probesetup is correct for the induction motor (a power factor of zero is notrealistic for induction motors and represents an extreme case).

Referring now to FIG. 12, a phasor bar 300 in accordance with thepresent invention is shown illustrating the per-phase voltages andcurrents of a synchronous motor at 0 leading or capacitant power factor.Such a situation is possible when the motor's rotor is deliberatelyover-excited at low load. Note that the current bars, 301, 302, 303appear to the left of the respective voltage bars 304, 305, 306 by a 90°power factor angle.

Referring now to FIGS. 16 and 17, FIG. 16 shows a prior art phasordiagram including a voltage phasor diagram 320 and a current phasordiagram 322 and FIG. 17 of the present invention includes a voltage barchart 324 and a current bar chart 326 with the bar charts 324, 326sharing a common horizontal axis 328. FIGS. 16 and 17 illustrate ascenario where the a and b current probes have been inadvertentlyinterchanged. Both FIGS. 16 and 17 illustrate this error by showinginconsistent a, b, c sequencing between the voltage and current diagrams320, 322 (FIG. 16) and 324, 326 (FIG. 17).

Referring now to FIGS. 18 and 19, respective phasor diagrams (FIG. 18)and phasor bar charts (FIG. 19) are shown which illustrate a probe setuperror in which the direction sense of the b current probe is wrong. BothFIGS. 18 and 19 illustrate a 180° phase shift and a greater than ±90°separation between voltage and current for the b phase.

Referring now to FIGS. 20 and 21, prior art phasors diagrams 340, 342are shown in FIG. 20 and bar charts of the present invention 344, 346are shown with a common horizontal axis 348 in FIG. 21. Both FIGS. 20and 21 illustrate a situation in which all three current probes havebeen installed backwards. Both FIGS. 20 and 21 indicate greater than 90°separation between each respective phase pair. It is believed that thebar diagram representations of the present invention (i.e. FIG. 21) morereadily illustrates something is amiss in the probe setup than the priorart voltage and current representations.

The bar diagrams of the present invention are easier in general tointerpret than the prior art phasor diagrams, and especially whenauditing the installation of probes or sensors. Further enhancements tothe bar graphs provide additional voltage and current information. Forinstance, making the bars nonlinear (but linear over a narrow interval)permits voltage and current unbalance and positioning the barshorizontally with respect to each other permits displaying phaserelationships.

From the foregoing description, it can be seen that the presentinvention comprises an improved method and apparatus for on-lineanalysis of polyphase electrical motors and their driven machines. Itwill be appreciated by those skilled in the art that changes could bemade to the embodiment described above without departing from the broadinventive concept thereof. It is understood, therefore, that thisinvention is not limited to the particular embodiment disclosed, but itis intended to cover modifications within the spirit and scope of thepresent invention as defined by the appended claims.

What is claimed is:
 1. A method of evaluating performance of a polyphaseinduction motor, the motor including a number of pole pairs, by usingdata from an uncoupled motor condition test and data acquired during acoupled motor condition test, comprising the steps of:(a) acquiringcurrent data by simultaneously sensing an instantaneous current signalsupplied to the motor as a function of time for all three electricalphases of the motor; (b) acquiring voltage data by simultaneouslysensing an instantaneous voltage signal supplied to the motor as afunction of time for all three electrical phases of the motor; (c)measuring individual motor stator resistances in both the uncoupledcondition and the coupled condition; (d) calculating slip from thecoupled test data; (e) calculating total real power dissipated by themotor in both the uncoupled condition and the coupled condition; (f)calculating stator I² R loss for both the coupled condition and theuncoupled condition, as the individual currents squared multiplied bythe respective individual stator resistances corresponding to theparticular motor operating condition; (g) estimating loss for theuncoupled condition as the total real power less the stator I² R losses;(h) estimating core loss as a percentage of the uncoupled loss; (i)calculating rotor I² R loss as the total real power less the stator I² Rloss less the estimated core loss, multiplied by slip; (j) determiningstray losses in accordance with a predetermined value based on a machinerating of the motor; and (k) calculating output power as the total realpower less the uncoupled loss less the stator I² R loss in the coupledcondition less the rotor I² R loss in the coupled condition and less theestimated stray losses.
 2. The method of claim 1 further comprising thestep of calculating motor efficiency as a ratio of the output power tothe total real power.
 3. The method of claim 1 further comprising thestep of calculating line I² R losses for the motor for the coupled anduncoupled conditions, wherein the calculated line I² R losses are alsosubtracted from the coupled and uncoupled total real power cases indetermining the output power.
 4. The method of claim 3 furthercomprising the step of calculating motor efficiency as a ratio of theoutput power to the total real power.
 5. The method of claim 1, furthercomprising the step of calculating power loss due to source unbalance bydirectly determining the negative sequence power wherein the calculatedpower loss due to source unbalance in the coupled and uncoupledconditions are also subtracted from the coupled and uncoupled total realpower conditions in determining the output power.
 6. The method of claim5 further comprising the step of calculating motor efficiency as a ratioof the output power to the total real power.